Polynomial Interpolation

Polynomial Interpolationis the interpolation of a given data set by a polynomial: given some points, find a polynomial which goes exactly through these points. When graphical data contains a gap, but data is available on either side of the gap or at a few specific points within the gap, an estimate of values within the gap can be made by interpolation. Polynomial interpolation is essential to perform sub-quadratic multiplication and squaring such as Karatsuba multiplication and Toom–Cook multiplication, where an interpolation through points on a polynomial which defines the product yields the product itself.

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